Their thinking does seem a bit muddled (and reading their word salad is like wading through treacle).
We have this:
As an explicitly feminist bookshop, at a time when there are fundamental disagreements in the movement, we feel it is important to re-state clearly that ours is an inclusive, intersectional feminism, and that we thus reject all politics that marginalize or target any woman, including trans women.
In our view, trans-exclusive rights campaigns, whether they call themselves feminist or use the term “gender-critical”, are reactionary rather than radical, and knowingly cause harm to women.
They give no explanation or justification for calling gender critical feminism 'reactionary' (perhaps because there isn't one) or how they think gender-critical feminism 'harms women'. Their so-called 'intersectional feminism' intersects with some men, but not with all women - transwomen are included, but gender-critical feminists are not. Since gender ideologues target some women (who they deride as TERFs), how can they claim to 'reject all politics that marginalize or target any woman'?
I'd also like to know what their definition of 'feminism' is. It doesn't seem to be one that I recognise. Feminism fights against gender stereotyping. Gender ideology worships it. How can they simultaneously be pro-feminism and pro-genderism?